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Identification Codes via Prime Numbers
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abstract
We introduce a method for construction of identification codes based on prime number generation over the noiseless channels. The earliest method for such construction based on prime numbers was proposed by Ahlswede which relies on algorithms for generation of prime numbers. This method requires knowledge of $2^n$ first prime numbers for identification codes with block length $n,$ which is not computationally efficient. In this work, we revisit Ahlswede's scheme and propose a number of modifications. In particular, employing probabilistic prime generation algorithm, we guarantee that the prime keys generation is possible in polynomial time. Furthermore, additional improvements in terms of type II upper bound are derived and presented. Finally, we propose a method for identification coding based on hash functions which generalizes the Ahlswede's scheme.
Forward citations
Cited by 3 Pith papers
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Identification for ISI Gaussian Channels
Identification capacity of ISI Gaussian channels permits super-exponential message growth ~2^(n log n R) even when ISI taps scale as n^κ for κ in [0, 1/2).
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Identification for Colored Gaussian Channels
Identification capacity bounds for colored Gaussian channels with polynomially bounded noise spectrum and sub-linear ISI memory allow super-exponential codebook growth of order 2^(n log n R).
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Identification for Inverse Gaussian Channels
Identification capacity of inverse Gaussian channels grows super-exponentially as ~2^(n log n R) under deterministic encoding and mild regularity on the first-arrival-time noise.
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